Infinite Sums | Geometric Series | Explained Visually

Geometric series are probably one of the first infinite sums that most of us encountered in high-school. When I first heard of an infinite sum(two or three years ago), I was really amazed that some of them would equal to a finite number. It seemed very strange that even if I keep adding numbers forever I would get a finite answer. At school I was just taught to plug the numbers into the formula, without fully understanding why or how it works.

In this video I go over some examples of geometric series and how we can get some insight on why it works by using visuals.

Thanks for watching~

P.S.
I will be moving to China for 5 months tomorrow, so I'm not sure if I will have an access to YouTube there, due to many sites being blocked by the government.

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Programs used:

- Cinema 4D

- Adobe Premiere Pro

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MUSIC:

A time of wonder

[antonmatei]

Started binge watching your videos and I feel like crying

[alwysrite]

thanks to 3Blue 1Brown for introducing me to this channel !

[ASCENDEDR]

jesus how do you not get more attention? this is beautiful

[drsuper]

Your work is amazing and I would call it "Mathematical poetry in motion". It should be used in all schools to motivate the kids and show them how majestic mathematics really is!

[saitaro]

Happy day: I found your channel, thanks 3b1b. The quality is impeccable, people like you should live forever.

[oxide]

The music along with the animation gives me chills. Good job!

[goncalosanhudodeportocarre]

And people say Mathematics isn't an Art.

[michaelrosenberg]

This is the first video I've watched from you.




It. Is. GLORIOUS!

[brutexx]

I'm honestly so glad I found your channel

[kandiriga]

Speechless only tears
Only tears in my eyes....
Thank you

[markkinnard]

You are seriously talented. The combination of great music and amazing geometry brings me to tears.

[kittenhero]

I didn't think it was possible to visualise the formula for the general arithmetic series

[DamaKubu]

feel like a child again, love it, so simple yet so elegant.

[Lawlophile]

You sir, are a credit to the world - especially to visual learners.

[abdulazizmemesh]

The best channel ever, there’s no other YouTube channel like you. Keep it up
It’s sad to see how this channel is really underrated.

[specialfalcon]

0:19 standing ovation man for that little animation!

[seemex]

It breaks my heart to see this channel sooo underrated. I don't usually write comments but you are different. Very beautiful content.

[mohammedal-haddad]

Proofs without words are the best. Thank you very much.

[vinayseth]

Thanks a ton for this! I was wondering the same about infinite sums and thought that I'd get my answer from a channel like Numberphile, but here you are with a simple, elegant and delightful visual presentation! 10/10! :)
PS: Thanks to you, I've now made it my agenda to apply this methodology to some infinite series that intrigue me personally. I don't have words to describe this newfound enthusiasm!

[AnonEMoose-mrjm]

Thoroughly enjoyable. The last one took me a bit longer to get but, once I did, I really understood what the geometric series was trying to convey. Very beautiful.